Geometric Data Analysis Based on Manifold Learning with Applications for Image Understanding

Miranda, Gastão Florêncio; Thomaz, Carlos Eduardo; Giraldi, Gilson A.

doi:10.1109/sibgrapi-t.2017.9

“…It is well known that the target dimensionality has big influence in the feature extraction step. Several methods for intrinsic dimensionality discovery of some dataset exist [5,7,10,22]. Future works may experiment with some of those discovery strategies such as exhaustive search guided by performance using SC and accuracy.…”

Section: Experiments and Resultsmentioning

confidence: 99%

Entropic principal component analysis using Cauchy–Schwarz divergence

Nakao

¹

,

Levada

²

2023

Knowl Inf Syst

0

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Dimensionality reduction has been explored to address the curse of dimensionality in high dimensional datasets of modern pattern recognition applications. In pattern recognition tasks, it is important to quantify how distinct two data samples are. Unsupervised metric learning serves for this purpose. In dimensionality reduction, a more adequate metric for a given dataset is implicitly learned. Principal Component Analysis is still the most used dimensionality reduction algorithm. Several modifications of this method have already been proposed as other algorithms belonging to the nonlinear class as well. However, all of them somehow rely on the Euclidean norm, which is known to fail in high dimensions and to be sensitive to outliers. So, in this paper, a new entropic approach was proposed, where the neighborhood of a data sample was mapped to an entropic space, where a stochastic divergence replaces the Euclidean. This approach was adopted to compute a new entropic covariance matrix that does not use inner product to estimate correlation between two features. A data sample neighborhood was mapped into an univariate Gaussian distribution and the statistical distance used was the Cauchy-Schwarz divergence. This new matrix was supplied to Principal Component Analysis classic algorithm. We compared the new method with existing linear and nonlinear algorithms. Using several real datasets, the comparison was made under two perspectives: cluster analysis and classification. Using a statistical test, it was possible to conclude that the new approach led to significant better results in both perspectives in comparison to all other algorithms considered.

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“…It is well known that the target dimensionality has big influence in the feature extraction step. Several methods for intrinsic dimensionality discovery of some dataset exist [5,7,10,22]. Future works may experiment with some of those discovery strategies such as exhaustive search guided by performance using SC and accuracy.…”

Section: Experiments and Resultsmentioning

confidence: 99%

Entropic Principal Component Analysis using Cauchy Schwarz divergence

Nakao

¹

,

Levada

²

2022

Preprint

1

0

View full text Add to dashboard Cite

Dimensionality reduction has been explored to address the curse of dimensionality in high dimensional datasets of modern pattern recognition applications. In pattern recognition tasks, it is important to quantify how distinct two data samples are. Unsupervised metric learning serves for this purpose. In dimensionality reduction, a more adequate metric for a given dataset is implicitly learned. Principal Component Analysis is still the most used dimensionality reduction algorithm. Several modifications of this method have already been proposed as other algorithms belonging to the nonlinear class as well. However, all of them somehow rely on the Euclidean norm, which is known to fail in high dimensions and to be sensitive to outliers. So, in this paper, a new entropic approach was proposed, where the neighborhood of a data sample was mapped to an entropic space, where a stochastic divergence replaces the Euclidean. This approach was adopted to compute a new entropic covariance matrix that does not use inner product to estimate correlation between two features. A data sample neighborhood was mapped into an univariate Gaussian distribution and the statistical distance used was the Cauchy-Schwarz divergence. This new matrix was supplied to Principal Component Analysis classic algorithm. We compared the new method with existing linear and nonlinear algorithms. Using several real datasets, the comparison was made under two perspectives: cluster analysis and classification. Using a statistical test, it was possible to conclude that the new approach led to significant better results in both perspectives in comparison to all other algorithms considered.

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Refined Deep Learning for Digital Objects Recognition via Betti Invariants

Onchiş

¹

,

Istin

²

,

Real

³

2019

Computer Analysis of Images and Patterns

1

0

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In this paper, we make use of the topological invariants of 2D images for an accelerated training and an improved recognition ability of a deep learning neural network applied to digital image objects. For our test images, we generate the associated simplicial complexes and from them we compute the Betti numbers which for a 2D object are the number of connected components and the number of holes. These information are used for training the network according to the corresponding Betti number. Experiments on the MNIST databases are presented in support of the proposed method.

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Geometric Data Analysis Based on Manifold Learning with Applications for Image Understanding

Cited by 8 publications

References 31 publications

Entropic principal component analysis using Cauchy–Schwarz divergence

Entropic principal component analysis using Cauchy–Schwarz divergence

Entropic Principal Component Analysis using Cauchy Schwarz divergence

Refined Deep Learning for Digital Objects Recognition via Betti Invariants

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